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Gene Ward Smith: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-11-22 10:22:56 UTC</tt>.<br>
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: The original revision id was <tt>385054582</tt>.<br>
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In mathematics, he has worked in the areas of [[http://en.wikipedia.org/wiki/Galois_theory|Galois theory]] and [[http://en.wikipedia.org/wiki/Monstrous_moonshine|Moonshine theory]].
In mathematics, he has worked in the areas of [[http://en.wikipedia.org/wiki/Galois_theory|Galois theory]] and [[http://en.wikipedia.org/wiki/Monstrous_moonshine|Moonshine theory]].


In music theory, he introduced [[http://en.wikipedia.org/wiki/Exterior_algebra|wedge products]] as a way of classifying [[regular temperaments]].  In this system, a temperament is specified by means of a [[Wedgies and Multivals|wedgie]], which may technically be identified as a point on a [[http://en.wikipedia.org/wiki/Grassmannian|Grassmannian]].  He has long drawn attention to the relationship between [[Equal Temperaments|equal divisions of the octave]] and the [[http://en.wikipedia.org/wiki/Riemann_zeta_function|Riemann zeta function]].&lt;ref&gt;Rusin, Dave. "Why 12 tones per octave?" http://www.math.niu.edu/~rusin/uses-math/music/12&lt;/ref&gt;&lt;ref&gt;OEIS. Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536&lt;/ref&gt;&lt;ref&gt;OEIS. Increasingly large integrals of the Z function between zeros http://oeis.org/A117538&lt;/ref&gt; He [[http://www.webcitation.org/67ZUSajSK|early on]] identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the [[http://x31eq.com/paradigm.html|regular mapping paradigm]].
In music theory, he introduced [[http://en.wikipedia.org/wiki/Exterior_algebra|wedge products]] as a way of classifying [[regular temperaments]].  In this system, a temperament is specified by means of a [[Wedgies and Multivals|wedgie]], which may technically be identified as a point on a [[http://en.wikipedia.org/wiki/Grassmannian|Grassmannian]].  He has long drawn attention to the relationship between [[Equal Temperaments|equal divisions of the octave]] and the [[The Riemann Zeta Function and Tuning|Riemann zeta function]].&lt;ref&gt;Rusin, Dave. "Why 12 tones per octave?" http://www.math.niu.edu/~rusin/uses-math/music/12&lt;/ref&gt;&lt;ref&gt;OEIS. Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536&lt;/ref&gt;&lt;ref&gt;OEIS. Increasingly large integrals of the Z function between zeros http://oeis.org/A117538&lt;/ref&gt; He [[http://www.webcitation.org/67ZUSajSK|early on]] identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the [[http://x31eq.com/paradigm.html|regular mapping paradigm]].


In the 1970s, Gene experimented with musical compositions using a device with four square-wave voices, whose tuning was very stable and accurate, being controlled by a [[http://en.wikipedia.org/wiki/Crystal_oscillator|crystal oscillator]]. The device in turn was controlled by HP [[http://en.wikipedia.org/wiki/HP_9800_series_desktop_computers|HP 9800 series desktop computers]], initially the HP 9830A, programmed in HP Basic, later the 9845A. Using this, he explored both just intonation with a particular emphasis on groups of transformations, and [[pajara]].  
In the 1970s, Gene experimented with musical compositions using a device with four square-wave voices, whose tuning was very stable and accurate, being controlled by a [[http://en.wikipedia.org/wiki/Crystal_oscillator|crystal oscillator]]. The device in turn was controlled by HP [[http://en.wikipedia.org/wiki/HP_9800_series_desktop_computers|HP 9800 series desktop computers]], initially the HP 9830A, programmed in HP Basic, later the 9845A. Using this, he explored both just intonation with a particular emphasis on groups of transformations, and [[pajara]].  
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In mathematics, he has worked in the areas of &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Galois_theory" rel="nofollow"&gt;Galois theory&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Monstrous_moonshine" rel="nofollow"&gt;Moonshine theory&lt;/a&gt;.&lt;br /&gt;
In mathematics, he has worked in the areas of &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Galois_theory" rel="nofollow"&gt;Galois theory&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Monstrous_moonshine" rel="nofollow"&gt;Moonshine theory&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In music theory, he introduced &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Exterior_algebra" rel="nofollow"&gt;wedge products&lt;/a&gt; as a way of classifying &lt;a class="wiki_link" href="/regular%20temperaments"&gt;regular temperaments&lt;/a&gt;.  In this system, a temperament is specified by means of a &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;, which may technically be identified as a point on a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Grassmannian" rel="nofollow"&gt;Grassmannian&lt;/a&gt;.  He has long drawn attention to the relationship between &lt;a class="wiki_link" href="/Equal%20Temperaments"&gt;equal divisions of the octave&lt;/a&gt; and the &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Riemann_zeta_function" rel="nofollow"&gt;Riemann zeta function&lt;/a&gt;.&lt;!-- ws:start:WikiTextRefRule:1:&amp;amp;lt;ref&amp;amp;gt;Rusin, Dave. &amp;amp;quot;Why 12 tones per octave?&amp;amp;quot; http://www.math.niu.edu/~rusin/uses-math/music/12&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-1" class="reference"&gt;&lt;a href="#cite_note-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:1 --&gt;&lt;!-- ws:start:WikiTextRefRule:3:&amp;amp;lt;ref&amp;amp;gt;OEIS. Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-2" class="reference"&gt;&lt;a href="#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:3 --&gt;&lt;!-- ws:start:WikiTextRefRule:5:&amp;amp;lt;ref&amp;amp;gt;OEIS. Increasingly large integrals of the Z function between zeros http://oeis.org/A117538&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-3" class="reference"&gt;&lt;a href="#cite_note-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:5 --&gt; He &lt;a class="wiki_link_ext" href="http://www.webcitation.org/67ZUSajSK" rel="nofollow"&gt;early on&lt;/a&gt; identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the &lt;a class="wiki_link_ext" href="http://x31eq.com/paradigm.html" rel="nofollow"&gt;regular mapping paradigm&lt;/a&gt;.&lt;br /&gt;
In music theory, he introduced &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Exterior_algebra" rel="nofollow"&gt;wedge products&lt;/a&gt; as a way of classifying &lt;a class="wiki_link" href="/regular%20temperaments"&gt;regular temperaments&lt;/a&gt;.  In this system, a temperament is specified by means of a &lt;a class="wiki_link" href="/Wedgies%20and%20Multivals"&gt;wedgie&lt;/a&gt;, which may technically be identified as a point on a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Grassmannian" rel="nofollow"&gt;Grassmannian&lt;/a&gt;.  He has long drawn attention to the relationship between &lt;a class="wiki_link" href="/Equal%20Temperaments"&gt;equal divisions of the octave&lt;/a&gt; and the &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning"&gt;Riemann zeta function&lt;/a&gt;.&lt;!-- ws:start:WikiTextRefRule:1:&amp;amp;lt;ref&amp;amp;gt;Rusin, Dave. &amp;amp;quot;Why 12 tones per octave?&amp;amp;quot; http://www.math.niu.edu/~rusin/uses-math/music/12&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-1" class="reference"&gt;&lt;a href="#cite_note-1"&gt;[1]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:1 --&gt;&lt;!-- ws:start:WikiTextRefRule:3:&amp;amp;lt;ref&amp;amp;gt;OEIS. Increasingly large peaks of the Riemann zeta function on the critical line http://oeis.org/A117536&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-2" class="reference"&gt;&lt;a href="#cite_note-2"&gt;[2]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:3 --&gt;&lt;!-- ws:start:WikiTextRefRule:5:&amp;amp;lt;ref&amp;amp;gt;OEIS. Increasingly large integrals of the Z function between zeros http://oeis.org/A117538&amp;amp;lt;/ref&amp;amp;gt; --&gt;&lt;sup id="cite_ref-3" class="reference"&gt;&lt;a href="#cite_note-3"&gt;[3]&lt;/a&gt;&lt;/sup&gt;&lt;!-- ws:end:WikiTextRefRule:5 --&gt; He &lt;a class="wiki_link_ext" href="http://www.webcitation.org/67ZUSajSK" rel="nofollow"&gt;early on&lt;/a&gt; identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the &lt;a class="wiki_link_ext" href="http://x31eq.com/paradigm.html" rel="nofollow"&gt;regular mapping paradigm&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the 1970s, Gene experimented with musical compositions using a device with four square-wave voices, whose tuning was very stable and accurate, being controlled by a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Crystal_oscillator" rel="nofollow"&gt;crystal oscillator&lt;/a&gt;. The device in turn was controlled by HP &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/HP_9800_series_desktop_computers" rel="nofollow"&gt;HP 9800 series desktop computers&lt;/a&gt;, initially the HP 9830A, programmed in HP Basic, later the 9845A. Using this, he explored both just intonation with a particular emphasis on groups of transformations, and &lt;a class="wiki_link" href="/pajara"&gt;pajara&lt;/a&gt;. &lt;br /&gt;
In the 1970s, Gene experimented with musical compositions using a device with four square-wave voices, whose tuning was very stable and accurate, being controlled by a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Crystal_oscillator" rel="nofollow"&gt;crystal oscillator&lt;/a&gt;. The device in turn was controlled by HP &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/HP_9800_series_desktop_computers" rel="nofollow"&gt;HP 9800 series desktop computers&lt;/a&gt;, initially the HP 9830A, programmed in HP Basic, later the 9845A. Using this, he explored both just intonation with a particular emphasis on groups of transformations, and &lt;a class="wiki_link" href="/pajara"&gt;pajara&lt;/a&gt;. &lt;br /&gt;
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